Non-contact measurement of a stress in a film on a substrate

ABSTRACT

A method for non-contact measurement of stress in a thin-film deposited on a substrate is disclosed. The method may include measuring first topography data of a substrate having a thin-film deposited thereupon. The method may also include comparing the first topography data with second topography data of the substrate that is measured prior to thin-film deposition. The method may further include obtaining a vertical displacement of the substrate based on the comparison between the first topography data and the second topography data. The method may also include detecting a stress value in the thin-film deposited on the substrate based on a fourth-order polynomial equation and the vertical displacement.

TECHNICAL FIELD

This disclosure generally relates to non-contact measurement of a stressin a film on a substrate.

BACKGROUND

Substrates having one or more layers of one or more thin-film materialdeposited thereupon may be used in many applications in the field ofelectronics. The thickness of such thin-film may range from about a fewhundred angstroms to several micrometers.

Due to a variety of reasons including for example, differences inproperties of the substrate material and that of the material used forthe thin-film deposition, mechanical stress may develop in thethin-film. Mechanical stress developed in the thin-film can be eithercompressive or tensile. In a substrate having the thin-film deposited ontop, development of compressive stress in the thin-film may cause thesubstrate to bow in a concave direction while development of tensilestress in the thin-film may cause the substrate to bow in a convexdirection. Thus, in instances in which a planar substrate is subjectedto thin-film deposition, compressive as well as tensile stressesdeveloped in the thin-film may cause a surface of the substrate todeviate from planarity. Mechanical stress in thin-films is a potentialcause of the substrate failure due to delamination and cracking ofthin-films.

SUMMARY

In accordance with one embodiment, a method for non-contact measurementof stress in a thin-film deposited on a substrate is disclosed. Themethod may include measuring first topography data of a substrate havinga thin-film deposited thereupon. The method may also include comparingthe first topography data with second topography data of the substratethat is measured prior to thin-film deposition. The method may furtherinclude obtaining a vertical displacement of the substrate based on thecomparison between the first topography data and the second topographydata. The method may also include detecting a stress value in thethin-film deposited on the substrate based on a fourth-order polynomialequation and the vertical displacement.

In accordance with an embodiment, the first topography data and thesecond topography data may include at least a curvature of the substratehaving the thin-film deposited thereupon and a curvature of thesubstrate prior to the thin-film deposition.

In accordance with another embodiment, each of the first topography dataand the second topography data may correspond to at least one predefineddiscrete point on the substrate.

In accordance with some embodiments, the method may include modelling ashape of the substrate prior to the thin-film deposition and a shape ofthe substrate having the thin-film deposited thereupon. The method mayalso include using the fourth-order polynomial equation and using afitting procedure to determine stress of the thin-film by fittingpolynomial parameters in the fourth-order polynomial equation.

In accordance with another embodiment, the method may include modellinga difference in a vertical position of the substrate at the at least onepredefined discrete point on the substrate prior to the thin-filmdeposition and a vertical position of the substrate at the at least onepredefined discrete point on the substrate after the thin-filmdeposition on the substrate. The method may also include using themodeled difference to detect stress in the thin-film.

In accordance with an embodiment, points of the at least one predefineddiscrete point may correspond to a region at about a center of thesubstrate and a further region of the substrate. The further region maybe away from the center of the substrate.

Further, in accordance with an embodiment, the fourth-order polynomialequation may include a first polynomial equation corresponding to acenter region of the substrate, the center region being proximate to acenter of symmetry of the substrate, and a second polynomial equationcorresponding to a further region of the substrate, the further regionbeing away from the center region of the substrate.

In one embodiment, the substrate may be supported from below by a firstedge defining element and a second edge defining element separated by apredefined separating value. The first and second edge defining elementsmay be positioned symmetrically with respect to an axis of thesubstrate.

In another embodiment, the substrate may be supported from below by atleast two parallel rows including a series of linearly placed edgedefining elements. The series of linearly placed edge defining elementsof each of the two parallel rows may be positioned symmetrically withrespect to an axis of the substrate.

In accordance with another embodiment, an apparatus for non-contactbased measurement of stress in a thin-film deposited on a substrate isdisclosed. The apparatus may include a topography measurement unitconfigured to determine topography data of a substrate. The apparatusmay also include a processor configured to compare first topography dataof the substrate having a thin-film deposited thereupon with secondtopography data of the substrate that is measured prior to the thin-filmdeposition. The processor may also be configured to obtain a verticaldisplacement of the substrate based on the comparison between the firsttopography data and the second topography data. The processor may alsobe configured to detect a stress value in the thin-film deposited on thesubstrate based on a fourth-order polynomial equation and the verticaldisplacement.

In accordance with another embodiment, an apparatus for non-contactbased measurement of stress in a thin-film deposited on a substrate isdisclosed. The apparatus may include multiple LED panels configured toemit a beam of light towards a surface of a substrate. The multiple LEDpanels may be arranged to include an opening at about a center of themultiple LED panels to allow flow of filtered air above the surface ofthe substrate. Further, the apparatus may include multiple camerasconfigured to capture a reflected beam of light that includes at least aportion of the emitted beam as reflected from the surface of thesubstrate. The apparatus may also include a detector unit to determinetopography data of the substrate prior to a thin-film deposition andafter the thin-film deposition on the substrate. The apparatus mayfurther include a processor. The detector unit may be configured todetect a change in an optical path of the reflected beam of light todetermine topography data of the substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings in which:

FIG. 1 illustrates a method of non-contact based measurement of stressin a thin-film deposited on a substrate, in accordance with anembodiment of the present disclosure;

FIG. 2 illustrates a method of non-contact based measurement of stressin a thin-film deposited on a substrate, in accordance with anembodiment of the present disclosure;

FIG. 3 illustrates a method of non-contact based measurement of stressin a thin-film deposited on a substrate, in accordance with anembodiment of the present disclosure;

FIG. 4 illustrates a glass panel supported on two edge definingelements, in accordance with an embodiment of the present disclosure;

FIG. 5 illustrates an apparatus for non-contact based measurement ofstress in a thin-film deposited on a substrate, in accordance with anembodiment of the present disclosure;

FIG. 6 illustrates an apparatus to determine a topography data of thesubstrate, in accordance with an embodiment of the present disclosure;

FIG. 7 illustrates a flat glass panel undergoing topography measurement,in accordance with an embodiment of the present disclosure;

FIG. 8 illustrates a bent glass panel undergoing topography measurement,in accordance with an embodiment of the present disclosure;

FIG. 9 illustrates a combined effect of the reflected beam of thesurface of the flat glass panel and bent glass panel, in accordance withan embodiment of the present disclosure thin-film

FIG. 10 illustrates measurement of an angle of incoming light from thesurface of a glass panel, in accordance with an embodiment of thepresent disclosure;

FIG. 11 illustrates a glass panel supported on two parallel rowsincluding a series of linearly placed edge defining elements, inaccordance with an embodiment of the present disclosure;

FIG. 12 illustrates a graph representing vertical displacements in asubstrate for various values of intrinsic stress in a thin-filmdeposited on the substrate, in accordance with an embodiment of thepresent disclosure; and

FIG. 13 illustrates a graph representing vertical displacements in thecenter and edges of the substrate, for various values of intrinsicstress in a thin-film deposited on the substrate, in accordance with anembodiment of the present disclosure.

DETAILED DESCRIPTION OF SOME EXAMPLE EMBODIMENTS

The present disclosure is directed to methods of detecting stress in athin-film deposited on a substrate. According to an aspect of anembodiment, a method for non-contact measurement of stress in athin-film deposited on a substrate based on fourth-order polynomialequations is provided. The fourth-order polynomial equations as providedin the present disclosure may be applicable to measurement of stress inthin-film deposited on glass panels and may be considered an approximatesolution for measurement of stress in a thin-film deposited on largeglass panels. Based on the measured shape of the thin-film depositedglass panel, a fitting procedure may be applied to the fourth-orderpolynomial equations to detect the value of stress. Further, the presentdisclosure also provides an apparatus including a topography measuringunit to measure the stress in a thin-film deposited on a glass panel.

According to an embodiment of the present disclosure, the fourth-orderpolynomial equations as provided in the present disclosure may includepolynomial parameters that may describe the shape of the substrate. Thevalues for these polynomial parameters may be determined by optimizingtotal potential energy acting upon the substrate. The values for thesepolynomial parameters, also referred to as coefficients in thisdisclosure, may be used to calculate shape of the substrate fordifferent values of stress. Then a fitting procedure can be applied todetermine stress in a substrate having thin film deposited thereuponbased on the shape of substrate under test, and the shapes thuscalculated, using the fourth order polynomial equations. The shape thuscalculated may also be referred to as a modelled shape in thisdisclosure. The foregoing description shall explain various embodimentsof the present disclosure which enable non-contact based measurement ofstress in a thin film deposited on the substrate.

FIG. 1 illustrates a method 100 of non-contact measurement of stress ina thin-film deposited on a substrate, in accordance with one embodiment.In one example, the substrate on which the method 100 is applicable maybe a glass panel. As illustrated in FIG. 1, the method 100 may begin atstep 101, measuring first topography data of a substrate having athin-film deposited thereupon. According to an embodiment of the presentdisclosure, the first topography data may be measured by one or moredevices including, but not limited to, interferometers, laser scanners,and techniques includes but not limited to, triangulation probes.

Further, the method 100 may include step 102, comparing the firsttopography data as obtained in step 101, with second topography data ofthe substrate that is measured prior to the thin-film deposition.According to one embodiment, the second topography data of the substratemay be measured prior to the thin film deposition on the substrate,using a similar technique that is used later for measuring the firsttopography data of the substrate. According to another embodiment, thesecond topography data of the substrate may be measured prior to thethin film deposition on the substrate, using one or more knowntechniques. In some embodiments, the first topography data may includethe measured curvature of the substrate having the thin-film depositedthereupon. In these and other embodiments, the second topography datamay include the measured curvature of the substrate prior to thethin-film deposition. Further, the method 100 may include step 103,obtaining a vertical displacement of the substrate based on thecomparison between the first topography data and the second topographydata in step 102. The vertical displacement of the substrate or theout-of-plane displacement of the substrate may be a result from anintrinsic stress in the thin-film formed upon the substrate. Theout-of-plane displacements in the substrate may occur in any or both ofthe two principal x-y directions within a horizontal plane lying in thesubstrate, and also along a third principal direction perpendicular tosaid plane. A substrate including vertical displacement as explainedherein shall be referred to as a ‘bent substrate’ hereafter in thisdisclosure.

Further, the method 100 may include step 104, detecting a stress valuein the thin-film deposited on the substrate based on one or morefourth-order polynomial equations and the vertical displacement obtainedin step 103. In some embodiments, the fourth-order polynomial equationsprovided in the present disclosure may represent the verticaldisplacements in the substrate within the two principal directionswithin a plane lying within the substrate and along the third principaldirection perpendicular to said plane. The fourth order polynomialequations shall be explained in detail in the foregoing description.

Modifications, additions, or omissions may be made to the method 100without departing from the scope of the present disclosure. For example,the operations of method 100 may be implemented in differing order.Additionally or alternatively, two or more operations may be performedat the same time. Furthermore, the outlined operations and actions areonly provided as examples, and some of the operations and actions may beoptional, combined into fewer operations and actions, or expanded intoadditional operations and actions without detracting from the essence ofthe disclosed embodiments.

FIG. 2 illustrates a method 200 of determining stress in the thin-filmon the substrate, wherein the first topography data and the secondtopography data include a corresponding curvature of the substrate. Themethod 200 may include step 201, modelling a shape of the substrateprior to the thin-film deposition, using fourth-order polynomialequations that may correspond to different regions as detailed below. Asexplained earlier in the present disclosure, a fourth-order polynomialequation includes polynomial parameters which may be determined tocalculate, or model, a shape of the substrate. Further, the method 200may include step 202, modelling a shape of the substrate having thethin-film deposited thereupon, using the fourth-order polynomialequations as used in step 201.

Further, the method 200 may include step 203, using a fitting-procedureto determine stress in the thin-film by fitting polynomial parameters inthe fourth-order polynomial equations, used in step 201 and step 202. Inone instance, the polynomial parameter is a predicted curvature of thesubstrate. The curvature of the substrate, as obtained from the measuredtopography, may be compared with curvature, as predicted from thefourth-order polynomial equations. Further, based on the comparedresults, a deviation between the measured curvature and the predictedcurvature may be obtained. Using the fitting-procedure, the deviationbetween the measured curvature and the predicted curvature is optimizedto obtain a value of a measured stress. In one example, the fittingprocedure used is a mean square fit or robust fit.

In one instance, the curvature of the substrate may include a verticaldisplacement at one or more prescribed positions on the substrate. Theone or more prescribed positions may be used to define respectivediscrete points on the substrate. In accordance with an embodiment, eachof the first topography data and the second topography data maycorrespond to at least one predefined discrete point on the substrate.In some embodiments, the first topography data and the second topographydata may represent a vertical position of the prescribed points. Inthese and other embodiments, the vertical position may be a positionwith respect to edge defining elements S1 and S2, on which the substratemay be supported, as explained later in the specification in relation toFIG. 4. Further, the predefined discrete points may correspond to eithera region at about a center of the substrate or a further region of thesubstrate. The further region may be away from the center region of thesubstrate. The center region can be a region proximate to a center ofsymmetry of the substrate. The further region can be a region proximateto the edges of the substrate.

Modifications, additions, or omissions may be made to the method 200without departing from the scope of the present disclosure. For example,the operations of method 100 may be implemented in differing order.Additionally or alternatively, two or more operations may be performedat the same time. Furthermore, the outlined operations and actions areonly provided as examples, and some of the operations and actions may beoptional, combined into fewer operations and actions, or expanded intoadditional operations and actions without detracting from the essence ofthe disclosed embodiments.

FIG. 3 illustrates a method 300 of determining stress in the thin-filmon the substrate, wherein the first topography data and the secondtopography data corresponds to at least one predefined discrete point onthe substrate. The method 300 may include step 301, measuring a firstvertical position of a predefined discrete point of the substrate, priorto the thin-film deposition. The method 300 may include step 302,measuring a second vertical position of the predefined discrete point ofthe substrate having the thin-film deposited thereupon. The firstvertical position and the second vertical position as measured may be inrelation to a particular predefined discrete point. The method 300 mayinclude step 303, modelling a difference in the first vertical positionand the second vertical position of the predefined discrete point of thesubstrate using a fourth-order polynomial equation. The method 300 mayinclude step 304, using the modeled difference to determine stress inthe thin-film. The stress may be determined using a similarfitting-procedure as disclosed above.

The foregoing description shall now explain the fourth-order polynomialequations, in accordance with various embodiments of the presentdisclosure. In accordance with some embodiments, the present disclosureprovides a first fourth-order polynomial equation corresponding to thecenter region of the substrate, and a second fourth-order polynomialequation corresponding to the further region of the substrate. However,it is understood that the fourth-order polynomials may be determined forand correspond to other regions on the substrate.

In some embodiments, the fourth-order polynomial equations may includecoefficients determined by optimizing a total potential energy actionupon the substrate having the thin film deposited thereupon. Further,the method 100 comprises of predicting a curvature of the substrateusing the determined coefficients.

FIG. 4 illustrates a structure of a flat glass panel 1, having a widthW, supported from below by a first edge defining element S1 and secondedge defining element S2. In some embodiments, the first and second edgedefining elements S1 and S2 are positioned symmetrically with respect toan axis of symmetry, denoted at point x=0, of a horizontal x-y planelying within the glass panel 1. As shown in FIG. 4 the two edge definingelements S1 and S2 are separated by a distance 2 a, the distance a beingmeasured from the axis of symmetry of the flat glass panel 1.

The following analytical equations are based on symmetry of thesubstrate, e.g., glass panel 1, as shown in FIG. 4.

In some embodiments, the shape of the substrate including verticaldisplacements is described by a function w(x), wherein w(x) is an evenfunction. In these and other embodiments, the fourth-order polynomialequations are based on the symmetry of the substrate as illustrated inFIG. 1. In these or other embodiments, the polynomial that maycorrespond to the center region the coefficients for the x̂1 or x̂3 termsmay be zero.

A first region I corresponding to a center region is considered. Thecenter region of the substrate lies between the two support points ‘−a’and ‘a’, referring the FIG. 4. In some embodiments, the first polynomialequation for a substrate supported by edge defining elements S1 and S2,separated by a distance 2 a, as shown in FIG. 4, is as follows:

w ₁(x)=(x−a)(x+a)(Q ₂ x ² +Q ₀) for x≥0,x≤a  (Equation 1)

wherein, w₁(x) is an even function representing the shape of thesubstrate, and where Q₂, Q₀ are unknown coefficients which will be foundwhen optimizing free energy of the glass.

The glass panel may also be divided into a second region II. The secondregion II may be a region further from the center region of thesubstrate from the support points to the edge of the glass panel. Theequation w(x) may also be a fourth-order polynomial equation whichequals zero at the support point located at x=a. In some embodiments,the second polynomial equation for a substrate supported by edgedefining elements S1 and S2, separated by a distance 2 a, as shown inFIG. 4, is as follows:

w ₂(x)=(x−a)(T ₀ +T ₁(x−a)¹ +T ₂(x−a)² +T ₃(x−a)³) for x>a  (Equation 2)

wherein, w₂(x) is an even function representing the shape of thesubstrate from the point a to the edge of the glass pane. The shape ofthe substrate may thus be described as:

w(x)=w ₁(x) for 0≤x≤a

w ₂(x) for x>a

In some embodiments, the function w(x) and the derivative of thefunction w(x),

$\frac{{dw}(x)}{dx}$

may be continuous at each point in general and at x=a in particular. Thecontinuity of

$\frac{{dw}(x)}{dx}$

at x=a implies:

$\frac{{dw}_{1}(x)}{dx} = \frac{{dw}_{2}(x)}{dx}$

at x=a. Solving this equation and substituting a for x, results in:

T ₀=2a(Q ₂ a ² +Q ₀)  (Equation 3)

For sufficiently small curvatures we can approximate curvature of theglass K by

$\kappa = \frac{d^{2}{w(x)}}{{dx}^{2}}$

The potential energy stored in the bent substrate plate per unit area isgiven by:

$\begin{matrix}{{E_{elasticplate} = {{Plate}\left( \frac{d^{2}{w(x)}}{{dx}^{2}} \right)}^{2}}{{{{where}\mspace{14mu} {Plate}} = {{EY}*{h^{3}/\left( {24\left( {1 - v^{2}} \right)} \right)}}},}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

where EY is Young's modulus,

h is glass plate thickness, and v is the Poisson's ratio.

The gravitational potential energy is:

E _(gravity)=Grav w(x)  (Equation 5)

where Grav=gρh

where g is free fall acceleration having usual value 9.8 m/s2, h is theglass plate thickness, and ρ is substrate plate density. It would beapparent to those skilled in the art that the density of the thin-filmhas been neglected which is usually justifiable approximation. Howeverit may be included by substituting ρh by surface density of thethin-film coated glass substrate.

The elastic energy density stored in a bent film is:

$\begin{matrix}{{E_{film} = {{Film}\frac{d^{2}{w(x)}}{{dx}^{2}}}}{{{{where}\mspace{14mu} {Film}} = {{- \left( \frac{h}{2} \right)}\; \sigma \; t}},}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

where tensile intrinsic stress in the thin-film σ has positive and t isthickness of thin-film. In some instances it may be assumed that thestress value σ does not change as a result of bending.

Total free energy density in the glass panel is equal to:

E=E _(elasticplate) +E _(gravity) +E _(film)  (Equation 7)

Therefore, the total energy in the glass panel per unit length indirection of Y-axis is equal

E _(TOT)=2∫₀ ^(W/2) E dx  (Equation 8)

By substituting Equation 7, and later Equations 6, 5, 4 into Equation 8we can express E_(TOT) as a function of w(x), and

$\frac{d^{2}{w(x)}}{{dx}^{2}}.$

$E_{TOT} = {2{\int_{0}^{W/2}{{E\left( {W,\frac{d^{2}w}{{dx}^{2}}} \right)}\ {dx}}}}$

where E is an algebraic function, and we can split the above integralinto two parts:

$E_{TOT} = {2\left\lbrack {{\int_{0}^{a}{{E\left( {W,\frac{d^{2}w}{{dx}^{2}}} \right)}\ {dx}}} + {\int_{a}^{W/2}{{E\left( {w,\frac{d^{2}w}{{dx}^{2}}} \right)}\ {dx}}}} \right\rbrack}$

By performing integrations using Equations 1, and 2, the followingequations are derived:

E _(TOT)=ƒ(Q ₀ ,Q ₂ ,T ₁ ,T ₂ ,T ₃)

where ƒ(Q₀,Q₂,T₁,T₂,T₃) is an algebraic function of its arguments. Itshould be noted that ƒ(Q₀,Q₂,T₁,T₂,T₃) does not depend on T₀ since itcan be defined in terms of Q₀,Q₂ as shown in Equation 3.

A minimum of function ƒ(Q₀,Q₂,T₁,T₂,T₃) may be found with respect to itsarguments. This leads to a following set of five linear equations:

$\quad\left\{ \begin{matrix}{\frac{\partial{f\left( {Q_{0},Q_{2},T_{1},T_{2},T_{3}} \right)}}{\partial Q_{0}} = 0} \\{\frac{\partial{f\left( {Q_{0},Q_{2},T_{1},T_{2},T_{3}} \right)}}{\partial Q_{2}} = 0} \\{\frac{\partial{f\left( {Q_{0},Q_{2},T_{1},T_{2},T_{3}} \right)}}{\partial T_{1}} = 0} \\{\frac{\partial{f\left( {Q_{0},Q_{2},T_{1},T_{2},T_{3}} \right)}}{\partial T_{2}} = 0} \\{\frac{\partial{f\left( {Q_{0},Q_{2},T_{1},T_{2},T_{3}} \right)}}{\partial T_{3}} = 0}\end{matrix} \right.$

This system of these five linear equations may be solved:

Q₀ = R[−(3W² − 12W a + 2a² + 24K)/96]$Q_{2} = {R\left\lbrack {- \frac{1}{48}} \right\rbrack}$T₁ = R(−(W² − 4Wa + 4 * a² + 8K)/32] T₂ = R[−(2a − W)/24]$T_{3} = {R\left\lbrack {- \frac{1}{48}} \right\rbrack}$

where

${= \frac{Grav}{Plate}},{{{and}\mspace{14mu} K} = {\frac{Film}{Grav}.}}$

Coefficients R and K may be measurements of strength of variouscomponents of potential energy.

Furthermore, using Equation 2 we can derive an explicit formula for T₀:

$T_{0} = {R\left\lbrack {{2\left( {- \frac{1}{48}} \right)a^{3}} + {a\left( \left\lbrack {{- \left( {{3W^{2}} - {12{Wa}} + {2a^{2}} + {24K}} \right)}/96} \right\rbrack \right)}} \right\rbrack}$or T₀ = R[+a([−(W² − 4Wa + 2a² + 8K)/32])]

The explicit analytical formulas of Q₀,Q₂,T₁,T₂,T₃, as disclosed above,enable us to calculate shape of the glass plate for given film andsubstrate parameters. Further, once fitting-procedure is applied, asdisclosed above, the intrinsic stress value may be determined at leastby analytical equation 6, as disclosed above.

Modifications, additions, or omissions may be made to FIG. 4 withoutdeparting from the scope of the present disclosure. For example, in someembodiments, FIG. 4 may include any number of other components that maynot be explicitly illustrated or described.

FIG. 5 illustrates a system 500 for non-contact based measurement ofstress in a thin-film deposited on a substrate. The system 500 mayinclude a topography measurement unit 501 and a computing system 502. Insome embodiments, the topography measurement unit 501 may be configuredto determine topography data of a substrate, prior to the thin-filmdeposition and after the thin-film deposition on the substrate, andcommunicate the determined topography data to the computing system 502.It should be understood that the topography measurement unit 501 mayinclude one or more known devices to measure topography data of thesubstrate. For example, the topography measurement unit 501 may include,but not limited to, interferometers, laser scanners and triangulationprobes. By way of an example, the topography measurement unit 501 mayinclude an apparatus 600, as shown in FIG. 6. FIG. 6 shall be explainedin the next section.

Further, the computing system 502 may be configured to detect a stressvalue in the thin-film deposited on the substrate in accordance with themethods as disclosed in FIGS. 1, 2, and 3. The system 500 as disclosedherein may provide real-time monitoring of stress as developed in athin-film-deposited on the substrate. The computing system 502 may befurther coupled to a display unit (not shown) for displaying results ofdata as processed according to the present disclosure. In some furtherembodiment, the results of the computing system 502 may be used tocontrol the thin-film deposition process on the substrate.

The computing system 502 may include a processor 550, a memory 552, anddata storage 554. The processor 550, the memory 552, and the datastorage 554 may be communicatively coupled.

In general, the processor 550 may include any suitable special-purposeor general-purpose computer, computing entity, or processing deviceincluding various computer hardware or software modules and may beconfigured to execute instructions stored on any applicablecomputer-readable storage media. For example, the processor 550 mayinclude a microprocessor, a microcontroller, a digital signal processor(DSP), an application-specific integrated circuit (ASIC), aField-Programmable Gate Array (FPGA), or any other digital or analogcircuitry configured to interpret and/or to execute program instructionsand/or to process data. Although illustrated as a single processor inFIG. 5, the processor 550 may include any number of processorsconfigured to, individually or collectively, perform or directperformance of any number of operations described in the presentdisclosure. Additionally, one or more of the processors may be presenton one or more different electronic devices, such as different servers.

In some embodiments, the processor 550 may be configured to interpretand/or execute program instructions and/or process data stored in thememory 552, the data storage 554, or the memory 552 and the data storage554. In some embodiments, the processor 550 may fetch programinstructions from the data storage 554 and load the program instructionsin the memory 552. After the program instructions are loaded into memory552, the processor 550 may execute the program instructions.

The memory 552 and the data storage 554 may include computer-readablestorage media for carrying or having computer-executable instructions ordata structures stored thereon. Such computer-readable storage media mayinclude any available media that may be accessed by a general-purpose orspecial-purpose computer, such as the processor 550. By way of example,and not limitation, such computer-readable storage media may includetangible or non-transitory computer-readable storage media includingRandom Access Memory (RAM), Read-Only Memory (ROM), ElectricallyErasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-OnlyMemory (CD-ROM) or other optical disk storage, magnetic disk storage orother magnetic storage devices, flash memory devices (e.g., solid statememory devices), or any other storage medium which may be used to carryor store particular program code in the form of computer-executableinstructions or data structures and which may be accessed by ageneral-purpose or special-purpose computer. Combinations of the abovemay also be included within the scope of computer-readable storagemedia. Computer-executable instructions may include, for example,instructions and data configured to cause the processor 550 to perform acertain operation or group of operations.

Modifications, additions, or omissions may be made to the system 500without departing from the scope of the present disclosure. For example,in some embodiments, system 500 may include any number of othercomponents that may not be explicitly illustrated or described.

FIG. 6 illustrates an example apparatus 600 which may be used to measurethe first topography data and the second topography data of thesubstrate, based on a triangulation probe technique. A similar techniqueto measure a shape of the glass panel 1, as described in Finot Et. Al inJ. Appl. Phys, volume 81, page 3457 (1997), may be applied by theapparatus 600 disclosed herein. However, in some embodiments, theapparatus 600 may include a modification to the apparatus as disclosedin Finot to incorporate a provision for clean-room applications. Detailsof such modification shall become apparent through the foregoingdisclosure.

The apparatus 600 may include a fan and a filter unit 640, a set ofcameras 601, an array of LED (light emitting diodes) positioned on, orbehind LED panels 602, supporting bars 603 supporting the LED panels, atool frame 605 to which the supporting bars 603 are attached. Further,the glass panel 1 may reside on edge defining elements S1 and S2. Edgedefining elements S1 and S2 may be attached to the tool frame 605.

The LED panels 602 may be configured to emit a beam of light towards asurface of the glass panel 1. As illustrated in FIG. 6, the LED panels602 are arranged in a slanted manner, to include an opening at about acenter for allowing flow of filtered air above the surface of the glasspanel 1. Further, the filtered air 641 may enter an enclosure defined bythe tool frame 605 as indicated by an arrow pointing towards the glasspanel 1. Thus, the arrangement illustrated in FIG. 6 may allow the flowof filtered air applicable for clean-room applications.

The cameras 601 may be configured to capture a reflected beam of lightthat includes at least a portion of the emitted beam as reflected from asurface of the glass plate 1. Although two cameras 601 are shown in FIG.1, a single camera 601 may also be used in some of the embodiments ofthe present disclosure.

Further, the apparatus 600 may include a detector unit 606 configured todetect topography data of the substrate prior to a thin-film depositionand after the thin-film deposition on the substrate. In someembodiments, the detector unit 606 may be configured to detect a changein optical path of the reflected beam of light to determine topographydata of the substrate. In one example, the LED panel 602 may be used todirect the emitted beam to the surface of the glass panel 1. When thereflective surface is curved, the reflected emitted beam is distortedand thereby the reflected beam acquires an optical path difference orphase change associated with the curvature of the surface of the glasspanel 1, under measurement. The pinhole camera 601 may capture eachpoint within the illuminated area on the surface of the glass panel.Thus, the curvature information at any point along any direction withinthe illuminated area can be obtained.

The foregoing description shall now explain an example of determiningtopography of a bent glass panel 1 vis-a v-s a flat glass panel, usingthe apparatus 600.

FIG. 7 illustrates a flat glass panel 1 undergoing topographymeasurement by the apparatus 600, illustrated in FIG. 6. As illustratedin FIG. 7, pinhole camera 601 receives a reflected beam. The reflectedbeam emanates from a point P on the flat glass panel 1, the point Pcorresponds to LED A from the LED panel 602 which can otherwise betreated as emanating from a virtual image A′. The pinhole camera 601 isconfigured to capture the reflected beam, which is supposedly making anangle α with respect to an imaginary normal line corresponding to thepinhole camera.

FIG. 8 illustrates a bent glass panel 1 undergoing topographymeasurement by the apparatus 600, illustrated in FIG. 6. As illustratedin FIG. 8, pinhole camera 601 receives a reflected beam. Because theglass panel 1 is bent, the reflected beam emanates from a point Q on thesurface of the bent glass panel which corresponds to LED A from the LEDpanel 602. Similar to FIG. 7 the pinhole camera 601 is configured tocapture the reflected beam which is supposedly making an angle β withrespect to an imaginary normal line corresponding to the pinhole camera.

FIG. 9 shows the reflected beams as emanating from the glass panel 1when flat and when bent. When the glass panel 1 is flat, the reflectedbeam emanates from a point P on the flat glass panel (which canotherwise be treated as emanating from a virtual image A′) and when theglass panel 1 is bent, the reflected beam emanates from a point Q on thebent glass panel (which can otherwise be treated as emanating from avirtual image A″). Thus, with respect to an imaginary normal linecorresponding to the pinhole camera 601 the reflected beam makes anangle α when the reflection is from a flat glass panel and makes anangle different α (β in this case) when the reflection is from a bentglass panel.

Apart from capturing the reflected beam, it is also possible to detectthe value of the angle which the reflected beam makes with the imaginarynormal line corresponding to the pinhole camera. Referring to FIG. 10,based on knowledge of: (a) a distance “f” between a point of entry ofthe reflected beam (into the pinhole camera) and a plane of formation ofthe image; and, (b) a distance “d” between a location of formation ofthe image P on the plane of formation of the image and a centre C of thepinhole camera, it is possible to calculate the value of the angle whichthe reflected beam makes with the imaginary normal line corresponding tothe pinhole camera.

Assuming that the glass panel was flat prior to the thin film depositionand if an angle of reflected beam is undergoing a change, then it can beinferred that the glass panel has become bent because of the stressesdeveloped in the thin-film. Also, a difference between the angles α andβ may be used to derive a vertical displacement as undergone by theglass panel because of the thin-film deposition. For example, more isthe vertical displacement; more will be the value of a differencebetween the angles α and β.

In particular, the angles α and β may be used to derive an extent ofbend in the glass panel, which may be contributed for example by theradius of curvature as developed in the glass panel because of thestress developed in the thin-film deposited thereupon. In particular,more is the radius of curvature as developed in the glass panel morewill be the value of a difference between the angles α and β.

In one example, the detector 606 may detect the topography of the glasspanel 1 based on the vertical displacement as derived from a differencebetween the angles α and β.

FIG. 12 illustrates another arrangement of support of a bent glass panel1. As shown in FIG. 12, the bent glass panel 1 is supported from belowby two parallel rows R1 and R2. In some embodiments, the row R1 mayinclude a series of linearly placed edge defining elements S1. In someembodiments, the row R2 may include a series of linearly placed edgedefining elements S2. The series of the edge defining elements S1 fromrow R1 and the series of edge defining elements S2 from row R2 may bepositioned symmetrically with respect to an axis of the glass panel,similar to the positioning of edge defining elements S1 and S2, as shownin FIG. 4. Although two rows have been illustrated in FIG. 12, the glasspanel may be supported by several such rows R1 and R2, each including aseries of linearly placed edge defining elements and the severalparallel rows being positioned symmetrically with respect to an axis ofthe glass panel. The support arrangement of the substrate as illustratedin FIG. 12 may help allow easier access of robot-end effectors to thesubstrate thus placed. The robot-end effectors may include effectorprongs that can easily insert between the rows of linearly placed edgedefining elements.

Numerical Results

A glass panel having the following physical characteristics isconsidered: Width W=1.85 m, Young's modulus EY=70.967E9 Pa, Poissonratio v=0.23, density p=2.37E3 kg/m³, thickness of the glass substrateh=0.7E−3 m, covered by film having thickness t=1E−6. On applying themethods of detecting stress in the thin-film deposited on the glasspanel, as provided in the present disclosure, it was found that anintrinsic stress of −500 MPa (dashed line), 0 MPa (solid line) and +500MPa (chain line), referring to a graph as illustrated in FIG. 12, haddeveloped at different prescribed points of the substrate having avertical displacement as shown in FIGS. 12 and 13, in presence ofgravity. The graph as illustrated in FIG. 12 and referred herein,represents the different prescribed points as horizontal position alongthe x-axis of the graph, assuming that the glass panel is positioned ona support arrangement as illustrated in FIG. 4. Further, the graphrepresents the vertical displacements for a prescribed point on theglass panel along the y-axis of the graph—The free fall acceleration isassumed as g=9.8 m/s2. Further, the glass panel is assumed to be arectangular shaped glass panel having dimensions 650 mm×550 mm.

Further, a graph illustrated in FIG. 13, illustrates the values ofintrinsic stress developed in the thin-film deposited on the glass panelfor different values of vertical displacement in the center region ofthe glass panel and regions near the edges of the glass panel. The graphas illustrated in FIG. 13 represents the values of intrinsic stressalong the x-axis of the graph, assuming that the glass panel ispositioned on a support arrangement as illustrated in FIG. 4. Further,the graph represents the values for the vertical displacements of theglass panel along the y-axis of the graph.

As used in the present disclosure, the terms “module” or “component” mayrefer to specific hardware implementations configured to perform theactions of the module or component and/or software objects or softwareroutines that may be stored on and/or executed by general purposehardware (e.g., computer-readable media, processing devices, etc.) ofthe computing system. In some embodiments, the different components,modules, engines, and services described in the present disclosure maybe implemented as objects or processes that execute on the computingsystem (e.g., as separate threads). While some of the system and methodsdescribed in the present disclosure are generally described as beingimplemented in software (stored on and/or executed by general purposehardware), specific hardware implementations or a combination ofsoftware and specific hardware implementations are also possible andcontemplated. In this description, a “computing entity” may be anycomputing system as previously defined in the present disclosure, or anymodule or combination of modulates running on a computing system.

Terms used in the present disclosure and especially in the appendedclaims (e.g., bodies of the appended claims) are generally intended as“open” terms (e.g., the term “including” should be interpreted as“including, but not limited to,” the term “having” should be interpretedas “having at least,” the term “includes” should be interpreted as“includes, but is not limited to,” etc.).

Additionally, if a specific number of an introduced claim recitation isintended, such an intent will be explicitly recited in the claim, and inthe absence of such recitation no such intent is present. For example,as an aid to understanding, the following appended claims may containusage of the introductory phrases “at least one” and “one or more” tointroduce claim recitations. However, the use of such phrases should notbe construed to imply that the introduction of a claim recitation by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim recitation to embodiments containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should be interpreted to mean “at least one”or “one or more”); the same holds true for the use of definite articlesused to introduce claim recitations.

In addition, even if a specific number of an introduced claim recitationis explicitly recited, those skilled in the art will recognize that suchrecitation should be interpreted to mean at least the recited number(e.g., the bare recitation of “two recitations,” without othermodifiers, means at least two recitations, or two or more recitations).Furthermore, in those instances where a convention analogous to “atleast one of A, B, and C, etc.” or “one or more of A, B, and C, etc.” isused, in general such a construction is intended to include A alone, Balone, C alone, A and B together, A and C together, B and C together, orA, B, and C together, etc.

Further, any disjunctive word or phrase presenting two or morealternative terms, whether in the description, claims, or drawings,should be understood to contemplate the possibilities of including oneof the terms, either of the terms, or both terms. For example, thephrase “A or B” should be understood to include the possibilities of “A”or “B” or “A and B.”

While the present subject matter has been described in detail withrespect to specific embodiments thereof, it will be appreciated thatthose skilled in the art, upon attaining an understanding of theforegoing, may readily produce alterations to, variations of, andequivalents to such embodiments. Accordingly, it should be understoodthat the present disclosure has been presented for-purposes of examplerather than limitation, and does not preclude inclusion of suchmodifications, variations, and/or additions to the present subjectmatter as would be readily apparent to one of ordinary skill in the art.

To the extent that method or apparatus embodiments herein are describedas having certain numbers of elements, it should be understood thatfewer than all of the elements may be necessary to define a completeclaim. I in addition, sequences of operations or functions described invarious embodiments do not require or imply a requirement for suchsequences in practicing any of the appended claims. Operations orfunctions may be performed in any sequence to effectuate the goals ofthe disclosed embodiments.

What is claimed is:
 1. A method of non-contact measurement of stress ina thin-film deposited on a substrate, the method comprising: measuringfirst topography data of a substrate having a thin-film depositedthereupon; comparing the first topography data with second topographydata of the substrate that is measured prior to the thin-filmdeposition; obtaining a vertical displacement of the substrate based onthe comparison between the first topography data and the secondtopography data; and detecting a stress value in the thin-film depositedon the substrate based on a fourth-order polynomial equation and thevertical displacement.
 2. The method as claimed in claim 1 wherein thefirst topography data and the second topography data include at least acurvature of the substrate having the thin-film deposited thereupon anda curvature of the substrate prior to the thin-film deposition,respectively.
 3. The method as claimed in claim 2 further comprising:modelling a shape of the substrate prior to the thin-film deposition anda shape of the substrate having the thin-film deposited thereupon, usingthe fourth-order polynomial equation; and using a fitting procedure todetermine stress of the thin-film by fitting polynomial parameters inthe fourth-order polynomial equation.
 4. The method as claimed in claim1 wherein each of the first topography data and the second topographydata corresponds to at least one predefined discrete point on thesubstrate.
 5. The method as claimed in claim 4 further comprising:modelling a difference in a vertical position of the substrate at the atleast one predefined discrete point on the substrate, the verticalposition being measured prior to the thin-film deposition and after thethin-film deposition on the substrate; and using the modeled differenceto detect stress in the thin-film.
 6. The method as claimed in claim 4wherein the at least one predefined discrete point corresponds to aregion at about a center of the substrate and a further region of thesubstrate, the further region being away from the center of thesubstrate.
 7. The method as claimed in claim 1 wherein the fourth-orderpolynomial equation includes: a first polynomial equation correspondingto a center region of the substrate, the center region being proximateto a center of symmetry of the substrate; and a second polynomialequation corresponding to a further region of the substrate, the furtherregion being away from the center region of the substrate.
 8. The methodas claimed in claim 1 wherein the fourth-order polynomial equationincludes coefficients determined by optimizing a total potential energyacting upon the substrate having the thin-film deposited thereupon. 9.The method as claimed in claim 8 comprising predicting a curvature ofthe substrate using the determined coefficients.
 10. The method asclaimed in claim 1 wherein the substrate is supported from below by afirst edge defining element and a second edge defining element separatedby a predefined separating value, the first and second edge definingelements being positioned symmetrically with respect to an axis of thesubstrate.
 11. The method as claimed in claim 1 wherein the substrate issupported from below by at least two parallel rows including a series oflinearly placed edge defining elements, the series of linearly placededge defining elements of each of the two parallel rows being positionedsymmetrically with respect to an axis of the substrate.
 12. An apparatusfor non-contact based measurement of stress in a thin-film deposited ona substrate, the apparatus comprising: a topography measurement unitconfigured to detect topography data of a substrate; and a processorconfigured to: compare first topography data of the substrate having athin-film deposited thereupon with second topography data of thesubstrate that is measured prior to the thin-film deposition; obtain avertical displacement of the substrate based on the comparison betweenthe first topography data and the second topography data; and detect astress value in the thin-film deposited on the substrate based on afourth-order polynomial equation and the vertical displacement.
 13. Theapparatus as claimed in claim 12 wherein the topography measurement unitcomprises: at least one LED panel configured to emit an emitted beam oflight towards the substrate; at least one camera configured to capture areflected beam of light that includes at least a portion of the emittedbeam as reflected from a surface of the substrate; and a detector unitconfigured to detect a change in optical path of the reflected beam oflight to determine topography data of the substrate.
 14. The method asclaimed in claim 13 wherein the substrate is supported from below by afirst edge defining element and a second edge defining element separatedby a predefined separating value, the first and second edge definingelements being positioned symmetrically with respect to an axis of thesubstrate.
 15. The method as claimed in claim 13 wherein the substrateis supported from below by at least two parallel rows including a seriesof linearly placed edge defining elements, the series of linearly placededge defining elements of each of the two parallel rows being positionedsymmetrically with respect to an axis of the substrate.
 16. Theapparatus as claimed in claim 12, wherein the fourth-order polynomialequation includes: a first polynomial equation corresponding to a centerregion of the substrate, the center region being proximate to a centerof symmetry of the substrate; and a second polynomial equationcorresponding to a further region of the substrate, the further regionbeing away from the center region of the substrate.
 17. An apparatus fornon-contact based measurement of stress in a thin-film deposited on asubstrate, the apparatus comprising: a plurality of LED panelsconfigured to emit an emitted beam of light towards a surface of asubstrate; the plurality of LED panels being arranged to include anopening at about a center for allowing flow of filtered air above thesurface of the substrate; a plurality of cameras configured to capture areflected beam of light that includes at least a portion of the emittedbeam as reflected from the surface of the substrate; a detector unit todetect topography data of the substrate prior to a thin-film depositionand after the thin-film deposition on the substrate, wherein thedetector unit is configured to detect a change in optical path of thereflected beam of light to determine topography data of the substrate;and a processor configured to cause performance of operationscomprising: compare first topography data of the substrate having athin-film deposited thereupon with second topography data of thesubstrate that is measured prior to the thin-film deposition; obtain avertical displacement of the substrate based on the comparison betweenthe first topography data and the second topography data; and detect astress value in the thin-film deposited on the substrate based on afourth-order polynomial equation and the vertical displacement.
 18. Theapparatus as claimed in claim 17 wherein the fourth-order polynomialequation includes: a first polynomial equation corresponding to a centerregion of the substrate, the center region being proximate to a centerof symmetry of the substrate; and a second polynomial equationcorresponding to a further region of the substrate, the further regionbeing away from the center region of the substrate.
 19. The apparatus asclaimed in claim 17 wherein the fourth-order polynomial equationincludes coefficients determined by optimizing a total potential energyacting upon the substrate having the thin-film deposited thereupon. 20.The method as claimed in claim 19 comprising predicting a curvature ofthe substrate using the determined coefficients.